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Natalka [10]
2 years ago
12

What point on the line y=9x+8 is closest to the origin

Mathematics
1 answer:
Marat540 [252]2 years ago
3 0

to find the point, find the location

realize that the shortest line that crosses through the origin and y=9x+8 is perpendicular to y=9x+8

perpendicular lines have slopes that multiply to get -1

y=9x+8 has a slope of 9

9*m=-1, m=-1/9

the slope of the mystery line is -1/9

since it passes through the origin, the y intercept is 0

y=(-1/9)x is the equation of the line from the point to the origin

find the intersection of this line and the original line

set them equal to each other

(-1/9)x=9x+8

multily both sides by 9

-x=81x+72

minus 81 both sides

-82x=72

divide both sides by -82

x=-36/41

find y

y=(-1/9)x

y=(-1/9)(-36/41)

y=4/41

the point is (\frac{-36}{41},\frac{4}{41})

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frozen [14]
Hi there!

A recipe for cake needs 3/4 of a cup of milk.
We are making 1/2 of the recipe, which means we also need half of the milk needed for the total recipe. Therefore, we can multiply 1/2 (half of the recipe) by 3/4 (the total amount of cups of milk needed for the total recipe).

\frac{1}{2} \times  \frac{3}{4} =  \frac{3  \times 1 }{2 \times 4} =  \frac{3}{8}
Hence, we need 3/8 cups of milk
4 0
2 years ago
to make 2 batches of nut nars, jayda needs to use 4 eggs how many eggs used in each batch of nut bars
muminat
To solve this problem, we need to set up a proportion.

2 batches of nut bars/ 4 eggs = 1 batch of nut bars / x eggs.

To solve this proportion, we use cross products, or multiplying the numerator of one number by the denominator of the other and setting them equal to one another.

(4 eggs) (1 batch) = (2 batches) (x eggs)

4= 2x

2=x

Therefore, 2 eggs are used in each batch of nut bars.
4 0
3 years ago
7. A dress that normally sells for $72 is on sale for $45. What is the percent decrease in the price? ​
ozzi

Actual price of the dress = 72

Selling price = 45

72 - 45 = $ 27

Percentage of decrease =

\frac{27}{72}  \times 100 \\

<h3>= <u>37.5%</u></h3>

.... Hope this will help.....

5 0
3 years ago
Read 2 more answers
When she drives to work, Samantha travels 10 miles in about 15 minutes. Matt travels 23 miles in about 30 minutes. Who has the f
Fantom [35]

Answer:

At 0.77 mi/min, Matt travels faster than Jennifer, who averages

only 0.67 mi/min.

Step-by-step explanation:

Average speed = distance/time

<em>For Samantha, </em>

Average speed = 10/15

Average speed = 0.67 mi/min

<em>For Matt, </em>

Average speed = 23/30

Average speed = 0.77 mi/min

7 0
3 years ago
Principle = $15,500 Interest Rate = 8.75% Time = ? Years Simple Interest = $5425.00
amid [387]
We must find time by using the simple interest formula:

I = P x i x t

I is the interest
P is the total principal 
i is the rate of interest per year
t is the total time in years

In this example, when we plug our known values in, our formula looks like this: 

t = \frac{I}{i*p}

t = \frac{5425}{0.0875 * 15500}

t = 4

So time (in years) would be 4 years. 
7 0
2 years ago
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